Which term is defined as smoothly pushing the camera directly forward towards the set?

The term that describes smoothly pushing the camera directly forward towards the set is indeed dolly in. This technique involves moving the camera on a wheeled platform, or dolly, to create a sense of intimacy and focus on the subject or action in the scene. When the camera moves closer to the subject, it can enhance the emotional impact and help the audience engage more deeply with what is happening on screen.

The other terms relate to different aspects of cinematography. Dolly out refers to moving the camera away from the subject, which creates a contrasting effect and typically results in the subject appearing smaller in the frame. A medium shot is a specific camera framing that usually shows a subject from the waist up, while a group shot captures multiple subjects within the frame but does not involve any specific camera movement technique like dolly in does.